Pigeonhole and Extremal Arguments · Challenge problem

A chess player plays at least one game a day for $77$ days and at most $132$ games in all. The proof that some run of consecutive days has exactly $21$ games looks at the partial sums $s_1 < s_2 < \cdots < s_{77}$ and the numbers $s_1 + 21, \ldots, s_{77} + 21$. These $154$ numbers all lie in $\{1, 2, \ldots, M\}$. What is $M$, the number of boxes?